Problem 90 - Chemistry A Molecular Approach

Question

Calculate the empirical formula for each natural flavor based on its elemental mass percent composition. a. methyl butyrate (component of apple taste and smell): \(\mathrm{C} 58.80 \%, \mathrm{H} 9.87 \%, \mathrm{O} 31.33 \%\) b. vanillin (responsible for the taste and smell of vanilla): \(\mathrm{C} 63.15 \%, \mathrm{H} 5.30 \%, \mathrm{O} 31.55 \%\)

Step-by-Step Solution

Answer

The empirical formula for methyl butyrate is C4H8O2, and for vanillin, it is C8H8O3.

Step 1: Calculate moles of each element in methyl butyrate

Convert the given mass percent composition of methyl butyrate into moles using the atomic mass of carbon (C), hydrogen (H), and oxygen (O). Assume a 100 g sample: Carbon: (58.80/12.01) mol, Hydrogen: (9.87/1.008) mol, Oxygen: (31.33/16.00) mol.

Step 2: Determine the simplest mole ratio for methyl butyrate

Divide each element's moles by the smallest number of moles calculated in step 1 to get the simplest whole number ratio. This gives the subscripts for the empirical formula.

Step 3: Calculate empirical formula for methyl butyrate

Use the ratios from step 2 to write the empirical formula, adjusting the subscripts to the nearest whole numbers if necessary.

Step 4: Calculate moles of each element in vanillin

Repeat steps 1 and 2 for vanillin, using its mass percent composition to convert to moles similarly.

Step 5: Determine the simplest mole ratio for vanillin

Divide each element's moles by the smallest mole number obtained for vanillin and find the simplest whole number ratio.

Step 6: Calculate empirical formula for vanillin

Use the ratios from step 5 to determine the empirical formula for vanillin, making sure to use whole numbers for subscripts.

Key Concepts

Stoichiometry

Stoichiometry is the cornerstone of chemical calculations. It revolves around the quantitative relationships between the reactants and products in a chemical reaction. Specifically, it's the study of the mole ratios and mass relationships between the elements and compounds in a chemical equation. When calculating the empirical formula of a substance like methyl butyrate, one essentially applies stoichiometric principles to determine the simplest whole-number ratio of atoms within the molecule.

Considering a sample mass allows for the conversion of percentage composition by mass into moles, which is vital because chemical reactions occur in mole ratios, not mass ratios. Assuming a 100 g sample simplifies this process by aligning mass percentages with actual gram measurements—58.80 grams of carbon translates directly to 58.80%, and so on. Then, by dividing by the respective atomic masses, the mole amounts are obtained, which are crucial in computing the empirical formula.

Molecular Composition

Understanding molecular composition is essential in the journey from elemental mass percentages to an empirical formula. Molecular composition describes the types and numbers of atoms present in a molecule. For simple compounds such as methyl butyrate and vanillin, one aims to discover the simplest integer ratio of the atoms that compose the compound, which provides insight into its molecular structure.

In the case of methyl butyrate, the atomic composition is conveyed through percentages: 58.80% carbon, 9.87% hydrogen, and 31.33% oxygen. By translating these percentages to moles and then finding the mole ratio, the molecular composition can be stated succinctly in terms of the empirical formula. This formula reflects the fundamental aspects of the molecular structure in the simplest form, important for understanding the substance's chemical behavior and properties.

Mole Ratio

The mole ratio is the heart of the empirical formula calculation and is a significant concept in chemistry. It compares the amounts of substances in moles, helping chemists to balance equations and determine reactant-product relationships. To find the empirical formula, one must first calculate the mole ratio of the elements present.

After converting the mass percentages into moles using atomic masses, the smallest mole quantity among the elements is identified. Dividing the number of moles of each element by this smallest number yields a mole ratio. If necessary, these ratios are adjusted to the nearest whole numbers to obtain the subscripts in the empirical formula. It's this mole ratio that provides a simple, whole-number ratio reflecting the proportional amount of each element, which is the essence of the empirical formula for any substance, such as the flavor components like methyl butyrate and vanillin.